A numerical study of magnetic reconnection in the large-Lundquist-number (S), plasmoid-dominated regime is carried out for S up to 107. The theoretical model of Uzdensky et al. [Phys. Rev. Lett. 105, 235002 (2010)] is confirmed and partially amended. The normalized reconnection rate is Ẽeff0.02 independently of S for S104. The plasmoid flux (Ψ) and half-width (wx) distribution functions scale as f(Ψ)Ψ-2 and f(wx)wx-2. The joint distribution of Ψ and wx shows that plasmoids populate a triangular region wxΨ/B0, where B0 is the reconnecting field. It is argued that this feature is due to plasmoid coalescence. Macroscopic “monster” plasmoids with wx10% of the system size are shown to emerge in just a few Alfvén times, independently of S, suggesting that large disruptive events are an inevitable feature of large-S reconnection.

1.
N. F.
Loureiro
,
A. A.
Schekochihin
, and
S. C.
Cowley
, “
Instability of current sheets and formation of plasmoid chains
,”
Phys. Plasmas
14
,
100703
(
2007
).
2.
G.
Lapenta
, “
Self-feeding turbulent magnetic reconnection on macroscopic scales
,”
Phys. Rev. Lett.
100
,
235001
(
2008
).
3.
W.
Daughton
,
V.
Roytershteyn
,
B. J.
Albright
,
H.
Karimabadi
,
L.
Yin
, and
K. J.
Bowers
, “
Transition from collisional to kinetic regimes in large-scale reconnection layers
,”
Phys. Rev. Lett.
103
,
065004
(
2009
).
4.
N. F.
Loureiro
,
D. A.
Uzdensky
,
A. A.
Schekochihin
,
S. C.
Cowley
, and
T. A.
Yousef
, “
Turbulent magnetic reconnection in two dimensions
,”
Mon. Not. R. Astron. Soc.
399
,
L146
(
2009
).
5.
R.
Samtaney
,
N. F.
Loureiro
,
D. A.
Uzdensky
,
A. A.
Schekochihin
, and
S. C.
Cowley
, “
Formation of plasmoid chains in magnetic reconnection
,”
Phys. Rev. Lett.
103
,
105004
(
2009
).
6.
A.
Bhattacharjee
,
Y.-M.
Huang
,
H.
Yang
, and
B.
Rogers
, “
Fast reconnection in high-Lundquist-number plasmas due to the plasmoid instability
,”
Phys. Plasmas
16
,
112102
(
2009
).
7.
P. A.
Cassak
,
M. A.
Shay
, and
J. F.
Drake
, “
Scaling of Sweet-Parker reconnection with secondary islands
,”
Phys. Plasmas
16
,
120702
(
2009
).
8.
Y.-M.
Huang
and
A.
Bhattacharjee
, “
Scaling laws of resistive magnetohydrodynamic reconnection in the high-Lundquist-number, plasmoid-unstable regime
,”
Phys. Plasmas
17
,
062104
(
2010
).
9.
D.
Biskamp
, “
Magnetic reconnection via current sheets
,”
Phys. Fluids
29
,
1520
(
1986
).
10.
N. F.
Loureiro
,
S. C.
Cowley
,
W. D.
Dorland
,
M. G.
Haines
, and
A. A.
Schekochihin
, “
X-point collapse and saturation in the nonlinear tearing mode reconnection
,”
Phys. Rev. Lett.
95
,
235003
(
2005
).
11.
P. A.
Sweet
, “
The neutral point theory of solar flares
,” in
Electromagnetic Phenomena in Cosmical Physics
, IAU Symposium, edited by
B.
Lehnert
(
1958
), Vol. 6, p.
123
.
12.
E. N.
Parker
, “
Sweet’s mechanism for merging magnetic fields in conducting fluids
,”
J. Geophys. Res.
62
,
509
, doi: (
1957
).
13.
D. A.
Uzdensky
,
N. F.
Loureiro
, and
A. A.
Schekochihin
, “
Fast magnetic reconnection in the plasmoid-dominated regime
,”
Phys. Rev. Lett.
105
,
235002
(
2010
).
14.
K.
Shibata
and
S.
Tanuma
, “
Plasmoid-induced-reconnection and fractal reconnection
,”
Earth, Planets Space
53
,
473
(
2001
).
15.
R. L.
Fermo
,
J. F.
Drake
, and
M.
Swisdak
, “
A statistical model of magnetic islands in a current layer
,”
Phys. Plasmas
17
,
010702
(
2010
).
16.
N.
Nishizuka
,
A.
Asai
,
H.
Takasaki
,
H.
Kurokawa
, and
K.
Shibata
, “
The power-law distribution of flare kernels and fractal current sheets in a solar flare
,”
Astrophys. J. Lett.
694
,
L74
(
2009
).
17.
J.
Lin
,
Y.-K.
Ko
,
L.
Sui
,
J. C.
Raymond
,
G. A.
Stenborg
,
Y.
Jiang
,
S.
Zhao
, and
S.
Mancuso
, “
Direct observations of the magnetic reconnection site of an eruption on 2003 November 18
,”
Astrophys. J.
622
,
1251
(
2005
).
18.
H. K.
Park
,
N. C.
Luhmann
, Jr.
,
A. J. H.
Donné
,
I. G. J.
Classen
,
C. W.
Domier
,
E.
Mazzucato
,
T.
Munsat
,
M. J.
van de Pol
, and
Z.
Xia
, “
Observation of high-field-side crash and heat transfer during sawtooth oscillation in magnetically confined plasmas
,”
Phys. Rev. Lett.
96
,
195003
(
2006
).
19.
Even in this case, the box is still much wider (in x) than the thickness of the SP layer, δSP/LS-1/23×10-4, and much longer (in y) than Lc/LSc/S10-3.
20.
When a typical plasmoid is ejected from its host layer into a bigger plasmoid, it is long and thin: wxwyẼeff (Ref. 13). However, immediately upon ejection, it is squashed against the bigger plasmoid and becomes circularized (wxwy), while preserving its flux and area. Thus, just before it starts coalescing with the bigger plasmoid, its width jumps up by a factor of Ẽeff-1/210, and its magnetic field becomes B0Ẽeff1/2 to preserve flux. This immediately moves the plasmoid vertically upwards by a factor Ẽeff-1/2 from the ULS diagonal. Our arguments can be modified to account for this effect—the result is to raise the threshold (2) upwards by a factor of order unity.
21.
M.
Bárta
,
J.
Büchner
,
M.
Karlický
, and
J.
Skála
, “
Spontaneous current-layer fragmentation and cascading reconnection in solar flares. I. Model and analysis
,”
Astrophys. J.
737
,
24
(
2011
).
22.
M.
Karlický
and
B.
Kliem
, “
Reconnection of a kinking flux rope triggering the ejection of a microwave and hard x-ray source i. observations and interpretation
,”
Sol. Phys.
266
,
71
(
2010
).
23.
W.
Daughton
,
V.
Roytershteyn
,
H.
Karimabadi
,
L.
Yin
,
B. J.
Albright
,
B.
Bergen
, and
K. J.
Bowers
, “
Role of electron physics in the development of turbulent magnetic reconnection in collisionless plasmas
,”
Nat. Phys.
7
,
539
(
2011
).
24.
H.
Karimabadi
,
J.
Dorelli
,
V.
Roytershteyn
,
W.
Daughton
, and
L.
Chacón
, “
Flux pileup in collisionless magnetic reconnection: Bursty interaction of large flux ropes
,”
Phys. Rev. Lett.
107
,
025002
(
2011
).
25.
W. H.
Matthaeus
and
S. L.
Lamkin
, “
Turbulent magnetic reconnection
,”
Phys. Fluids
29
,
2513
(
1986
).
26.
A.
Lazarian
and
E. T.
Vishniac
, “
Reconnection in a weakly stochastic field
,”
Astrophys. J.
517
,
700
(
1999
).
27.
G.
Lapenta
and
L.
Bettarini
, “
Spontaneous transition to a fast 3D turbulent reconnection regime
,”
Europhys. Lett.
93
,
65001
(
2011
).
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